The utilization of vortex generators to increase heat transfer from cylinders installed inside a duct is investigated. In particular, a channel containing eight cylinders with volumetric heat sources is considered for different values of the Reynolds number. The effective possibility to use vortex generators with different sizes to increase heat transfer and, consequently, reduce the surface temperature of the cylinders is examined. Also, the amount of pressure drop inside the channel due to the presence of vortex generators is considered and compared with the cases without vortex generators. The results show that although the addition of generators increases the pressure drop, it strongly contributes to increase the heat transfer coefficient inside the duct (up to 80–90%).

In today’s world, one of the essential human concerns is reducing energy consumption and consequently reducing fossil fuels consumption. On the one hand, the limited energy resources and, on the other hand, air pollution due to the excessive use of fossil fuels have led researchers to study and introduce various methods to reduce energy consumption. One of the most important ways to reduce energy consumption is to use techniques to increase heat transfer [

One of the most important applications is to increase heat transfer in cooling systems. Cooling is one of the most important parts of design in various industries, which in the absence of temperature management in the operation of temperature systems can lead to early depreciation and failure of these systems or cause irreparable disasters. Numerous articles on cooling systems of applications in various industries have been presented by researchers [

Numerous methods have been introduced by researchers to increase the heat transfer and cooling of temperature systems. In general, methods of increasing heat transfer can be divided into two categories: passive and active. In the passive method, no external forces are used to transfer heat, and therefore no energy is spent on cooling the system, but in the active method, external forces are used to increase heat transfer. Although the amount of heat transferred is generally higher in active methods than in passive methods, but in active methods we have to spend external energy to increase the amount of heat transferred. Therefore, one of the important advantages of using passive methods is that there is no need to consume additional energy to increase heat transfer. For example, Zharfa et al. [

Various techniques can be introduced as a passive method to increase heat transfer. These include changes in the roughness of the pages [

In the present study, Vertex Generator has been used to increase the cooling of the cylinders installed inside the closed channel. Although many researches have been done by researchers in order to increase the heat transfer by Vertex Generator, but the design of Vertex Generator has been done in this research for cooling cylinders with arrangement in which heat is generated in volume in previous researches. Therefore, in this study, to increase the heat transfer and cooling of the cylinders, different vortex generators have been added to the system and its effects have been compared with the case where no generator vortex has been used in the system.

^{3}. The inlet fluid enters the channel from the left at different speeds at a temperature of 20°C and leaves the channel from the right after passing through the channel and cooling the cylinders. Inside the channel, vortex generators have been used to increase the rate of heat transfer and cooling of most cylinders, and the effects of using vortex generators in the absence of vortex generators have been compared and investigated.

Forced entry of fluid into the channel at different speeds and Reynolds and passing it around the cylinders causes the cylinder to cool. Due to the fact that the operating fluid is in the water channel and considering the low Reynolds numbers for the inlet fluid in the channel, Navier–Stokes relations for the fluid flow are considered as incompressible fluid with viscous dynamicsand a steady state condition. PISO procedure for pressure-velocity calculation in the Navier-Stokes equations has been adapted to this steady-state problem [

where ρ is the density of the fluid, t is the time, u is the velocity of the fluid, p is the pressure, and μ is the viscosity of the fluid inside the channel. For incompressible fluid, we will have the continuity equation as follows:

To calculate the Reynolds number at the channel input, we have the following relation:

where V is the average velocity of the fluid at the channel inlet and D_{h} is the hydraulic diameter of the channel inlet, which is obtained from the following equation:

where a and b are the length and width of the channel. To obtain the temperature distribution inside the channel as well as the amount of heat transferred from the cylinders to the fluid, we will have the following energy relationship:

In this regard, Cp is the specific heat capacity of the fluid at constant pressure, T is the fluid temperature, k is the coefficient of thermal conductivity which takes different values according to whether it is evaluated in the fluid or inside the (solid) cylinders, and q_{s} is the amount of heat produced per unit volume inside the cylinders. q_{s} takes a non-zero value only inside the cylinders, and it is set to zero otherwise.

The following equation is used to compare the vortex performance of generators to calculate the heat transfer coefficient of displacement within the channel.

Q is the total heat transferred from the cylinders, h is the average heat transfer coefficient of the fluid movement inside the channel and ∆T is the temperature difference between the inlet fluid Tin and the average temperature on the surface of the cylinders Ts, which is obtained from the following equation:

To better compare the rate of increase in heat transfer due to the use of vortex generators, the Nusselt dimensionless number is used, which is obtained from the following equation:

To solve the fluid flow relations, the boundary conditions determined in this case are as follows: the left side of the velocity inlet channel and the right side of the velocity outlet channel, and the upper walls and cylinder surfaces are considered to be wall-to-wall with the principle of non-slip. To solve the energy equations, the input of the left channel below is considered as a constant temperature at 20°C and the output of the right is as an outlet. The upper and lower walls of the duct are designated as heat insulators and the cylinders are designated as heat sources per unit volume. Thermal conduction was considered for solid phases and thermal convection was considered for the fluid phase.

To solve this problem, COMSOL Multiphysics commercial software has been used, which is based on the Finite-element method. A non-uniform free-triangular grid was used to network the problem geometry and to solve the problem independently of the network effects; different elements were performed and compared with the average temperature on the cylinders in a state that is shown in

Case | Number of elements | Average temperature on slender surface (K) |
---|---|---|

1 | 6452 | 523.25 |

2 | 8648 | 535.37 |

3 | 10902 | 537.73 |

4 | 13744 | 538.43 |

In this section, the simulation and discussion of the results by creating the vortex of generators on the fluid motion path and by changing the fluid motion path and directing it on cylindrical cylinders was presented. It was used to enhance the heat transfer of the cylinders to the fluid flow to reduce the average surface temperature of the closed channels, which are in good agreement with the results of reference [

In

In this paper, by creating the vortex of generators on the fluid motion path and by changing the fluid motion path and directing it to cylindrical cylinders, we try to increase the heat transfer from the cylinders to the fluid flow to reduce the average surface temperature of the cylinders:

With increasing fluid velocity, the amount of heat transfer increases, but this amount does not show a significant number due to the alignment of the cylinders.

Adding the vortex of generators increases heat transfer due to the direction of more excellent fluid around the cylinders.

As the vortex size of the generators increases due to the increase in the transfer of cool fluid around the cylinders, the heat transfer rate also increases significantly.

By adding the vortex of generators and increasing their size, the Reynolds number increases due to reducing the cross-sectional area of the channel through which the fluid flows.

Increasing the Reynolds number due to adding the generators’ vertex if the fluid flow changes from slow to turbulent initially reduces the Nusselt number but return to the uptrend.

In addition to increasing the pressure drop inside the channel due to the increase in fluid velocity, by adding the vertex of the generators, the amount of pressure drop inside the channel is also increased.

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